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Homological properties of the enveloping algebra U(Sl2)

Published online by Cambridge University Press:  24 October 2008

J. T. Stafford
J. T. Stafford
Affiliation:
Gonville and Caius College, Cambridge
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Extract

In this paper we will study the homological properties of the enveloping algebra U = U (Sl2(ℂ)), with particular reference to the homological dimension of simple U-modules and the global dimension of the primitive factor rings of U.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 1 , January 1982 , pp. 29 - 37
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Anderson, F. W. and Fuller, K. R.Rings and categories of modules (Graduate Texts in Mathematics, no. 13, Springer-Verlag, Berlin, New York, 1974).CrossRefGoogle Scholar
(2)Arnal, D. and Pinczon, G.Idéaux à gauche dans dea quotients simples de l'algèbre enveloppante de sl(2). Bull. Soc. Math. France 101 (1973), 381–395.Google Scholar
(3)Bernstein, J. N. and Gelfand, S. I.Tensor products of finite and infinite dimensional representations of semi-simple Lie algebras. Compositio Math. 41 (1980), 245–285.Google Scholar
(4)Bhatwadekar, S.On the global dimension of some filtered algebras. J. London Math. Soc. 13 (1976), 239–248.Google Scholar
(5)Borho, W. and Rentschler, R.Oresche Teilmengen in Einhullenden Algebren. Math. Ann. 217 (1975), 201–210.Google Scholar
(6)Cartan, H. and Eilenberg, S.Homological algebra (Princeton University Press, Princeton, 1956).Google Scholar
(7)Dixmier, J.Enveloping algebras (North Holland, Amsterdam, 1977).Google Scholar
(8)Dixmier, J.Quotients simple de l'algèbre enveloppante de sl 2. J. Algebra. 24 (1973), 551–564.Google Scholar
(9)Fields, K. L.On the global dimension of skew polynomial rings – an addendum. J. Algebra 14 (1970), 528–530.Google Scholar
(10)Rentschler, R. and Gabriel, P.Sur la dimension dea anneaux et ensembles ordonnés. C.R. Acad. Sci. Paris (A) 265 (1967), 712–715.Google Scholar
(11)Roos, J.-E.Compléments a l'étude des quotients primitifs des algèbres enveloppantes des algèbres de Lie semi-simples. C.R. Acad. Sci. Paris (A), 276 (1973), 447–450.Google Scholar
(12)Rotman, J. J.An introduction to homological algebra (Academic Press, London, 1979).Google Scholar
(13)Smith, S. P.The primitive factor rings of the enveloping algebra of sl(2, C) Proc. London Math. Soc. 24 (1981), 97–108.Google Scholar
(14)Stafford, J. T.Completely faithful modules and ideals of simple Noetherian rings. Bull. London Math. Soc. 8 (1976), 168–173.Google Scholar
(15)Stafford, J. T.Stable structure of noncommutative Noetherian rings. J. Algebra. 47 (1977), 244–267.CrossRefGoogle Scholar
(16)Stafford, J. T.Generating modules efficiently: Algebraic K-theory for noncommutative Noetherian rings. J. Algebra 69 (1981), 312–346.Google Scholar